Lesson 4


Scatterplots and Perceived Audience Size

Notes:


library(ggplot2)
setwd('/Users/Yuji/Library/Mobile Documents/com~apple~CloudDocs/Course/Data Analysis with R')
pf <- read.csv("pseudo_facebook.tsv", sep = '\t')

Scatterplots

Notes:

ggplot(aes(x = age, y = friend_count), data = pf) +
  geom_point()


What are some things that you notice right away?

Response: People under 30 tend to have much more friends than other age group. ***

ggplot Syntax

Notes:

ggplot(aes(x = age, y = friend_count), data = pf) +
  geom_point() +
  xlim(13, 90)
## Warning: Removed 4906 rows containing missing values (geom_point).


Overplotting

Notes:

ggplot(aes(x = age, y = friend_count), data = pf) +
  geom_jitter(alpha = 1/20) +
  xlim(13, 90)
## Warning: Removed 5186 rows containing missing values (geom_point).

What do you notice in the plot?

Response: The noise is less and we can see the pattern in the group under 30. Most of the friends count of people under 30 is less than 1000. ***

Coord_trans()

Notes:

ggplot(aes(x = age, y = friend_count), data = pf) +
  geom_jitter(alpha = 1/20) +
  xlim(13, 90) +
  coord_trans(y = "sqrt") +
  ylim(0, 5000)
## Warning: Removed 6142 rows containing missing values (geom_point).

Look up the documentation for coord_trans() and add a layer to the plot that transforms friend_count using the square root function. Create your plot!

What do you notice?

The bottom line is not straight now, and the y scale is not equal. ***

Alpha and Jitter

Notes:

ggplot(aes(x=age, y = friendships_initiated), data = pf) +
  geom_point(alpha = 1/10, position = position_jitter(h = 0))


Overplotting and Domain Knowledge

Notes:


Conditional Means

Notes:

library(dplyr)
## 
## Attaching package: 'dplyr'
## 
## The following object is masked from 'package:stats':
## 
##     filter
## 
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
age_groups <- group_by(pf, age)
pf.fc_by_age <- summarise(age_groups,
                          friend_count_mean = mean(friend_count),
                          friend_count_median = median(friend_count),
                          n = n())
pf.fc_by_age <- arrange(pf.fc_by_age, age)
head(pf.fc_by_age)
## Source: local data frame [6 x 4]
## 
##   age friend_count_mean friend_count_median    n
## 1  13          164.7500                74.0  484
## 2  14          251.3901               132.0 1925
## 3  15          347.6921               161.0 2618
## 4  16          351.9371               171.5 3086
## 5  17          350.3006               156.0 3283
## 6  18          331.1663               162.0 5196
pf.fc_by_age <- pf %>%
  group_by(age) %>%
  summarise(friend_count_mean = mean(friend_count),
            friend_count_median = median(friend_count),
            n = n()) %>%
  arrange(age)

Create your plot!

ggplot(aes(x = age, y = friend_count_mean), data = pf.fc_by_age) +
  geom_line()


Overlaying Summaries with Raw Data

Notes:

ggplot(aes(x=age, y = friend_count), data = pf) +
  coord_cartesian(xlim = c(13, 70), ylim = c(0, 1000)) +
  geom_point(alpha = 1/20, 
             position = position_jitter(h = 0),
             color = 'orange') +
  geom_line(stat = "summary", fun.y = mean) +
  geom_line(stat = "summary", fun.y = quantile, probs = 0.1,
            linetype = 2, color = "blue") +
  geom_line(stat = "summary", fun.y = quantile, probs = 0.5,
            color = "blue") +
  geom_line(stat = "summary", fun.y = quantile, probs = 0.9,
            linetype = 2, color = "blue")

What are some of your observations of the plot?

Response: The 10% quantile is the most flat line, other than that, other 3 lines have same trends. ***

Moira: Histogram Summary and Scatterplot

See the Instructor Notes of this video to download Moira’s paper on perceived audience size and to see the final plot.

Notes:


Correlation

Notes:

cor.test(x = pf$age, y = pf$friend_count)
## 
##  Pearson's product-moment correlation
## 
## data:  pf$age and pf$friend_count
## t = -8.6268, df = 99001, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.03363072 -0.02118189
## sample estimates:
##         cor 
## -0.02740737

Look up the documentation for the cor.test function.

What’s the correlation between age and friend count? Round to three decimal places. Response:


Correlation on Subsets

Notes:

with(subset(pf, age <= 70), cor.test(age, friend_count))
## 
##  Pearson's product-moment correlation
## 
## data:  age and friend_count
## t = -52.5923, df = 91029, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.1780220 -0.1654129
## sample estimates:
##        cor 
## -0.1717245

Correlation Methods

Notes:


Create Scatterplots

Notes:

ggplot(aes(y = likes_received, x = www_likes_received), data = pf) +
  geom_point(alpha = 1/10) +
  coord_cartesian(ylim = c(0,quantile(pf$likes_received, 0.95)), 
                  xlim = c(0, quantile(pf$www_likes_received, 0.95))) +
  geom_smooth(method = "lm", color = "red")


Strong Correlations

Notes:

What’s the correlation betwen the two variables? Include the top 5% of values for the variable in the calculation and round to 3 decimal places.

with(pf, cor.test(likes_received, www_likes_received))
## 
##  Pearson's product-moment correlation
## 
## data:  likes_received and www_likes_received
## t = 937.1035, df = 99001, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.9473553 0.9486176
## sample estimates:
##       cor 
## 0.9479902

Response:


Moira on Correlation

Notes:


More Caution with Correlation

Notes:

library(alr3)
## Loading required package: car
data(Mitchell)
ggplot(aes(y = Temp, x = Month), data = Mitchell) +
  geom_point()

Create your plot!

with(Mitchell, cor.test(Month, Temp))
## 
##  Pearson's product-moment correlation
## 
## data:  Month and Temp
## t = 0.8182, df = 202, p-value = 0.4142
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.08053637  0.19331562
## sample estimates:
##        cor 
## 0.05747063

Noisy Scatterplots

  1. Take a guess for the correlation coefficient for the scatterplot.

  2. What is the actual correlation of the two variables? (Round to the thousandths place)


Making Sense of Data

Notes:

ggplot(aes(y = Temp, x = Month), data = Mitchell) +
  geom_point() +
  scale_x_discrete(breaks = seq(0, 203, 12))

ggplot(aes(x=(Month%%12),y=Temp),data=Mitchell)+ 
  geom_point()


A New Perspective

What do you notice? Response:

Watch the solution video and check out the Instructor Notes! Notes:


Understanding Noise: Age to Age Months

Notes:


Age with Months Means

pf$age_with_months <- pf$age + (12-pf$dob_month)/12

Programming Assignment

pf.fc_by_age_months <- pf %>%
  group_by(age_with_months) %>%
  summarise(friend_count_mean = mean(friend_count),
            friend_count_median = median(friend_count),
            n = n()) %>%
  arrange(age_with_months)

group_age_months <- group_by(pf, age_with_months)
pf.fc_by_age_months <- summarise(group_age_months,
                                 friend_count_mean = mean(friend_count),
            friend_count_median = median(friend_count),
            n = n())
pf.fc_by_age_months <- arrange(pf.fc_by_age_months, age_with_months)

Noise in Conditional Means

ggplot(aes(x = age_with_months, y = friend_count_mean), data = subset(pf.fc_by_age_months, age_with_months < 71)) +
  geom_line()


Smoothing Conditional Means

Notes:

p1 <- ggplot(aes(x = age_with_months, y = friend_count_mean), data = subset(pf.fc_by_age_months, age_with_months < 71)) +
  geom_line() +
  geom_smooth()

p2 <- ggplot(aes(x = age, y = friend_count_mean), data = subset(pf.fc_by_age, age < 71)) +
  geom_line() +
  geom_smooth()

p3 <- ggplot(aes(x = round(age / 5) * 5, y = friend_count),
             data = subset(pf, age < 71)) +
  geom_line(stat = "summary", fun.y = "mean")

library(gridExtra)
## Loading required package: grid
grid.arrange(p1,p2,p3, ncol=1)
## geom_smooth: method="auto" and size of largest group is <1000, so using loess. Use 'method = x' to change the smoothing method.
## geom_smooth: method="auto" and size of largest group is <1000, so using loess. Use 'method = x' to change the smoothing method.


Which Plot to Choose?

Notes:


Analyzing Two Variables

Reflection:


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